There is no universal legal definition of hate speech. In general, it is communication used to intentionally harm any identifiable group including those categorized by ethnicity, gender, sexual orientation, or religion. The response of the Christian should depend on what part of the many definitions is being used:
How should Christians view hate speech? What does the Bible say?
Communication designed to incite hate, violence, and/or prejudicial action.
The Bible says that Christians are called to peace (Matthew 5:9; 1 Corinthians 7:15). We absolutely should not try to rile up hate or violence in or toward a people group. "Prejudicial action," however, is an ill-defined slippery slope. If the choice is between absolute liberty and God's standards, we should follow God's standards.
It is wrong to use words to incite others to hate Muslims, but it is also wrong to allow Muslims the freedom of religion in matters that contradict human rights such as honor killings and child brides.
Expressions regarded as offensive to a group of people or hurtful to their feelings.
Romans 12:18 says, "If possible, so far as it depends on you, live peaceably with all." While we should not seek to be offensive, our priority is to the truth. Living our faith should be done sensitively without compromising fact or biblical truth.
When visiting Thailand, it is inappropriate to insult or disrespect the king, but as believers, we remember our true King is Jesus.
Expressions that are degrading to a group of people.
All people are made in the image of God (Genesis 1:27). Jesus specifically said we are not to call another a degrading name (Matthew 5:22).
It is appropriate to say that a group and its members hold unbiblical or incorrect beliefs, but it is not appropriate to call them stupid.
Communication that justifies, denies, or minimizes harm done to such a group.
It is just foolish to rate the pain of a group when we do not have firsthand knowledge of what they have gone through. And insisting the harm did not take place ranges from intentional ignorance to outright lying.
It is wrong to minimize or deny how homosexuals have been hurt by the careless or malicious words of Christians; it is possible and good to acknowledge and apologize for the harm caused by ungodly reactions to sin.
The Bible is clear that Christians should love their neighbors (Matthew 22:37-40), not speak about or to them hatefully. Where the problem comes in is with society's definition of "hate." We are to be respectful, forgiving, and peaceable, but we are also to speak the truth. The most hateful speech a Christian can indulge in is speech that pushes another farther from God's truth and love.
This leads us to the other side of the coin. It is inevitable in this fallen world that those who reject God will communicate that rejection in ways that disparage His followers. Jesus told us to expect persecution (2 Timothy 3:12), that it is a sign that we are His followers (John 15:18-19). But He also gave us an example as to how we should respond: "When he was reviled, he did not revile in return; when he suffered, he did not threaten, but continued entrusting himself to him who judges justly" (1 Peter 2:23). Likewise, Jesus told us that if someone insults us, we should respond mildly and without offense (Matthew 5:38-39).
And the Bible tells us why: "And the Lord's servant must not be quarrelsome but kind to everyone, able to teach, patiently enduring evil, correcting his opponents with gentleness. God may perhaps grant them repentance leading to a knowledge of the truth, and they may come to their senses and escape from the snare of the devil, after being captured by him to do his will" (2 Timothy 2:24-26). Every word we speak and every reaction we give to the words spoken to us should be measured against this goal: to lead others to the knowledge of the truth.
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